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1.
Подробнее
Aldibekov, T. М
Nonlinear differential equation with first order partial derivatives [Текст] / T.М Aldibekov, M. M. Aldazharova // Әл-Фараби атындағы Қазақ ұлттық университет = Вестник Казахского национального университета им.Аль-Фараби. - Аlmaty, 2018. - №3. - Р. 3-11. - (Математика, механика, информатика сериясы = Серия математика, механика, информатика)
ББК 22.2
Рубрики: Механика
Кл.слова (ненормированные):
теңдеу -- бірінші ретті дербес туындылар -- дифференциалдық теңдеу -- Алдибеков Т.М -- Алдажарова М.М -- Хабаршы-Вестник
Аннотация: Туындылардың бiреуiне байланысты шешiлген бiрiншi реттi дербес туындылы сызықты емес дифференциалдық теңдеудiң шешiмдерiнiң асимптотикалық мiнезi зерттеледi. Бiрiншi реттi дербес туындылы дифференциалдық теңдеудiң әрқайсысының қандайда бiр шарттарда фундаменталды интегрладар жүйесi немесе интегралдық базисi болады. Айта кететiнi, жалпы бiрiншi реттi сызықты дербес туындылы дифференциалдық теңдеудiң тривиалды емес интегралы болмауы да мұмкiн. Бiрiншi реттi сызықты дербес туындылы дифференциалдық теңдеу үшiн, оның коэффициенттерi шенелмеген жиында берiлiп, үзiлiссiз бiрiншi реттi дербес туындылары болса және бiрiншi коэффициентi бiрге тең болса, интегралды базис бар болады. Бұл жүмыста туындылардың бiреуiне байланысты шешiлген бiрiншi реттi дербес туындылы сызықты емес дифференциалдық теңдеу екi жағынан бiрiншi реттi дербес туындылы дифференциалдық теңдеулермен бағаланады. Дифференциалдық теңсiздiктердi пайдалана отырып, туындылардың бiреуiне байланысты шешiлген бiрiншi реттi дербес туындылы сызықты емес теңдеудiң тәуелсiз айнымалыларнының бiреуi плюс шексiздiкке ұмтылған жағдайда нөлге ұмтылатын шешiмi бар болатыны дәлелденген. Қазiргi таңда дербес туындылы дифференциалдық теңдеулер теориясы жаратылыс танудың түрлі салаларында өз қолданыстарын табуда.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Aldazharova, M.M.
Aldibekov, T. М
Nonlinear differential equation with first order partial derivatives [Текст] / T.М Aldibekov, M. M. Aldazharova // Әл-Фараби атындағы Қазақ ұлттық университет = Вестник Казахского национального университета им.Аль-Фараби. - Аlmaty, 2018. - №3. - Р. 3-11. - (Математика, механика, информатика сериясы = Серия математика, механика, информатика)
Рубрики: Механика
Кл.слова (ненормированные):
теңдеу -- бірінші ретті дербес туындылар -- дифференциалдық теңдеу -- Алдибеков Т.М -- Алдажарова М.М -- Хабаршы-Вестник
Аннотация: Туындылардың бiреуiне байланысты шешiлген бiрiншi реттi дербес туындылы сызықты емес дифференциалдық теңдеудiң шешiмдерiнiң асимптотикалық мiнезi зерттеледi. Бiрiншi реттi дербес туындылы дифференциалдық теңдеудiң әрқайсысының қандайда бiр шарттарда фундаменталды интегрладар жүйесi немесе интегралдық базисi болады. Айта кететiнi, жалпы бiрiншi реттi сызықты дербес туындылы дифференциалдық теңдеудiң тривиалды емес интегралы болмауы да мұмкiн. Бiрiншi реттi сызықты дербес туындылы дифференциалдық теңдеу үшiн, оның коэффициенттерi шенелмеген жиында берiлiп, үзiлiссiз бiрiншi реттi дербес туындылары болса және бiрiншi коэффициентi бiрге тең болса, интегралды базис бар болады. Бұл жүмыста туындылардың бiреуiне байланысты шешiлген бiрiншi реттi дербес туындылы сызықты емес дифференциалдық теңдеу екi жағынан бiрiншi реттi дербес туындылы дифференциалдық теңдеулермен бағаланады. Дифференциалдық теңсiздiктердi пайдалана отырып, туындылардың бiреуiне байланысты шешiлген бiрiншi реттi дербес туындылы сызықты емес теңдеудiң тәуелсiз айнымалыларнының бiреуi плюс шексiздiкке ұмтылған жағдайда нөлге ұмтылатын шешiмi бар болатыны дәлелденген. Қазiргi таңда дербес туындылы дифференциалдық теңдеулер теориясы жаратылыс танудың түрлі салаларында өз қолданыстарын табуда.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Aldazharova, M.M.
2.
Подробнее
22
M85
Moremedi G.M.
Necessary and Sufficient Conditions for Oscillations of Functional Differential Equations [Текст] / Moremedi G.M. // Әл-Фараби атындағы қазақ ұлттық университеті = Казахский национальный университет имени Аль-Фараби = Al-Farabi Kazakh national university. - Аlmaty, 2018. - №3. - P. 12-23. - (Journal of Mathematics, Mechanics, Computer Science = Серия математика, механика, информатика)
ББК 22
Рубрики: Физико-математические науки
Кл.слова (ненормированные):
Колебание -- запаздывание -- необходимые и достаточные условия -- характеристическое уравнение -- разностные уравнения -- Moremedi. G.M -- Stavroulakis.I.P -- Zhunussova.Zh.Kh
Аннотация: В этой статье представлены необходимые и достаточные условия для колебаний всех решений запаздывающих, продвинутых и нейтральных дифференциальных уравнений первого и высшего порядка с одним или несколькими постоянными коэффициентами и постоянными аргументами в терминах характеристического уравнения. Явные (только по постоянному коэффициенту и постоянному аргументу) необходимые и достаточные условия также представлены в случае одного аргумента. В случае уравнения n-го порядка необходимые и достаточные условия для колебаний всех решений представлены когда n является нечетным, а необходимые и достаточные условия для колебаний всех граничных решений представлены когда n является четным. В этом случае явные достаточные условия для колебаний всех решений представлены когда n является нечетным, а явные достаточные условия для колебаний всех граничных решений для уравнений с запаздыванием и всех неграничных решений для продвинутных уравнений представлены когда n является нечетным. В случае нескольких аргументы явные, но достаточные условия даются, и результаты также распространяется на уравнения с несколькими переменными коэффициентами. Ключевые слова: Колебание; запаздывание, необходимые и достаточные условия, характеристическое уровнение, разностные уравнения.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Stavroulakis, I.P.
Zhunussova, Zh.Kh
M85
Moremedi G.M.
Necessary and Sufficient Conditions for Oscillations of Functional Differential Equations [Текст] / Moremedi G.M. // Әл-Фараби атындағы қазақ ұлттық университеті = Казахский национальный университет имени Аль-Фараби = Al-Farabi Kazakh national university. - Аlmaty, 2018. - №3. - P. 12-23. - (Journal of Mathematics, Mechanics, Computer Science = Серия математика, механика, информатика)
Рубрики: Физико-математические науки
Кл.слова (ненормированные):
Колебание -- запаздывание -- необходимые и достаточные условия -- характеристическое уравнение -- разностные уравнения -- Moremedi. G.M -- Stavroulakis.I.P -- Zhunussova.Zh.Kh
Аннотация: В этой статье представлены необходимые и достаточные условия для колебаний всех решений запаздывающих, продвинутых и нейтральных дифференциальных уравнений первого и высшего порядка с одним или несколькими постоянными коэффициентами и постоянными аргументами в терминах характеристического уравнения. Явные (только по постоянному коэффициенту и постоянному аргументу) необходимые и достаточные условия также представлены в случае одного аргумента. В случае уравнения n-го порядка необходимые и достаточные условия для колебаний всех решений представлены когда n является нечетным, а необходимые и достаточные условия для колебаний всех граничных решений представлены когда n является четным. В этом случае явные достаточные условия для колебаний всех решений представлены когда n является нечетным, а явные достаточные условия для колебаний всех граничных решений для уравнений с запаздыванием и всех неграничных решений для продвинутных уравнений представлены когда n является нечетным. В случае нескольких аргументы явные, но достаточные условия даются, и результаты также распространяется на уравнения с несколькими переменными коэффициентами. Ключевые слова: Колебание; запаздывание, необходимые и достаточные условия, характеристическое уровнение, разностные уравнения.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Stavroulakis, I.P.
Zhunussova, Zh.Kh
3.
Подробнее
22.1
A30
Akhmet, M. U
Әл - Фараби ат. ҚҰУ Хабаршы = Вестник КазНУ им Аль - Фараби [Текст] / M.U Akhmet // Singularly perturbed linear oscilator with piecewise-constant argument . - Алматы, 2018. - №1(97). - Р. 3-13. - (Journal of Mathematics, Mechanics, Computer Science = Серия математика, механика, информатика)
ББК 22.1
Рубрики: Математика
Кл.слова (ненормированные):
кусочно-постоянный аргумент обобщенного типа -- малый параметр -- сингулярное возмущение
Аннотация: The Cauchy problem for singularly perturbed linear differential equation the second order withpiecewise-constant argument is considered in the article. The definition of singularly perturbedlinear harmonic oscillator with piecewise-constant argument is given in the paper. The system offundamental solutions of homogeneous singularly perturbed differential equation with piecewise-constant argument are constructed according to the nonhomogeneous singularly perturbed differ-ential equation with piecewise-constant argument. With the help of the system of fundamentalsolutions, the initial functions are constructed and their asymptotic representation are obtained.By using the reduction method, the analytical formula of the solution of singularly perturbed theinitial value problem with piecewise-constant argument is obtained. In addition, the unperturbedCauchy problem is constructed according to the singularly perturbed Cauchy problem. The so-lution of the unperturbed Cauchy problem is obtained. When the small parameter tends to thezero, the solution of singularly perturbed the Cauchy problem with piecewise-constant argumentapproaches the solution of the unperturbed Cauchy problem with piecewise-constant argument.The theorem on the passage to the limit is proved.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Dauylbaev, M.K
Mirzakulova, A.E
Atakhan, N.
A30
Akhmet, M. U
Әл - Фараби ат. ҚҰУ Хабаршы = Вестник КазНУ им Аль - Фараби [Текст] / M.U Akhmet // Singularly perturbed linear oscilator with piecewise-constant argument . - Алматы, 2018. - №1(97). - Р. 3-13. - (Journal of Mathematics, Mechanics, Computer Science = Серия математика, механика, информатика)
Рубрики: Математика
Кл.слова (ненормированные):
кусочно-постоянный аргумент обобщенного типа -- малый параметр -- сингулярное возмущение
Аннотация: The Cauchy problem for singularly perturbed linear differential equation the second order withpiecewise-constant argument is considered in the article. The definition of singularly perturbedlinear harmonic oscillator with piecewise-constant argument is given in the paper. The system offundamental solutions of homogeneous singularly perturbed differential equation with piecewise-constant argument are constructed according to the nonhomogeneous singularly perturbed differ-ential equation with piecewise-constant argument. With the help of the system of fundamentalsolutions, the initial functions are constructed and their asymptotic representation are obtained.By using the reduction method, the analytical formula of the solution of singularly perturbed theinitial value problem with piecewise-constant argument is obtained. In addition, the unperturbedCauchy problem is constructed according to the singularly perturbed Cauchy problem. The so-lution of the unperturbed Cauchy problem is obtained. When the small parameter tends to thezero, the solution of singularly perturbed the Cauchy problem with piecewise-constant argumentapproaches the solution of the unperturbed Cauchy problem with piecewise-constant argument.The theorem on the passage to the limit is proved.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Dauylbaev, M.K
Mirzakulova, A.E
Atakhan, N.
4.
Подробнее
22.1
M75
Mirzakulova, A. E
The Cauchy problem for sinqularly perturbed hiqher-order inteqro-differential equations [Текст] / A.E Mirzakulova // Әл - Фараби ат. ҚҰУ Хабаршы = Вестник КАЗНУ им Аль - Фараби. - Алматы, 2018. - №1(97). - Р. 14-24. - (Математика, механика, информатика сериясы = Серия математика, механика, информатика)
ББК 22.1
Рубрики: Математика
Кл.слова (ненормированные):
сингулярное возмущение -- малый параметр -- начальные функции -- асимптотика -- предельный переход
Аннотация: The article is devoted to research the Cauchy problem for singularly perturbed higher-order linearintegro-differential equation with a small parameter at the highest derivatives, provided that theroots of additional characteristic equation have negative signs. The aim of this paper is to bringasymptotic estimation of the solution of a singularly perturbed Cauchy problem and the asymptoticconvergence of the solution of a singularly perturbed initial value problem to the solution ofan unperturbed initial value problem. In this paper the fundamental system of solutions, initialfunctions of a singularly perturbed homogeneous differential equation are constructed and theirasymptotic estimates are obtained. By using the initial functions, we obtain an explicit analyticalformula of the solution. The theorem about asymptotic estimate of a solution of the initial valueproblem is proved. The unperturbed Cauchy problem is constructed. We find the solution of theunperturbed Cauchy problem. An estimate difference of the solution of a singularly perturbedand unperturbed initial value problems. The asymptotic convergence of solution of a singularlyperturbed initial value problem to the solution of the unperturbed initial value problem is proved.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Dauylbaev, M.K
Akhmet, M.U
Dzhetpisbaeva, A.K
M75
Mirzakulova, A. E
The Cauchy problem for sinqularly perturbed hiqher-order inteqro-differential equations [Текст] / A.E Mirzakulova // Әл - Фараби ат. ҚҰУ Хабаршы = Вестник КАЗНУ им Аль - Фараби. - Алматы, 2018. - №1(97). - Р. 14-24. - (Математика, механика, информатика сериясы = Серия математика, механика, информатика)
Рубрики: Математика
Кл.слова (ненормированные):
сингулярное возмущение -- малый параметр -- начальные функции -- асимптотика -- предельный переход
Аннотация: The article is devoted to research the Cauchy problem for singularly perturbed higher-order linearintegro-differential equation with a small parameter at the highest derivatives, provided that theroots of additional characteristic equation have negative signs. The aim of this paper is to bringasymptotic estimation of the solution of a singularly perturbed Cauchy problem and the asymptoticconvergence of the solution of a singularly perturbed initial value problem to the solution ofan unperturbed initial value problem. In this paper the fundamental system of solutions, initialfunctions of a singularly perturbed homogeneous differential equation are constructed and theirasymptotic estimates are obtained. By using the initial functions, we obtain an explicit analyticalformula of the solution. The theorem about asymptotic estimate of a solution of the initial valueproblem is proved. The unperturbed Cauchy problem is constructed. We find the solution of theunperturbed Cauchy problem. An estimate difference of the solution of a singularly perturbedand unperturbed initial value problems. The asymptotic convergence of solution of a singularlyperturbed initial value problem to the solution of the unperturbed initial value problem is proved.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Dauylbaev, M.K
Akhmet, M.U
Dzhetpisbaeva, A.K
5.
Подробнее
32.81
B19
Balakayeva , G. T
Mathematical and numerical modeling of transfer processes in the cleaning ofexhaust gases in an automobile neutralizer [Текст] / G.T Balakayeva // Әл - Фараби ат. ҚҰУ Хабаршы = Вестник КазНУ им Аль - Фараби. - Алматы, 2018. - №1(97). - Р. 127-133. - (Математика, механика, информатика сериясы=Серия математика, механика, информатика. Journal of Mathematics, Mechanics, Computer Science.)
ББК 32.81
Рубрики: Информатика
Кл.слова (ненормированные):
нейтрализатор -- каталитический нейтрализатор -- итерационный метод -- метод прогонки
Аннотация: Every year, the atmosphere in Kazakhstan is polluted approximately 5-7 million tons of pollutants,about a third of which belong to the vehicle. Also excess pollution of the air basin of the cities ofthe Republic is caused by pollution of pollutants by metallurgy, oil refining and chemical industryfactories, automobile and railway transport. The harmful substances emitted by motor transportadversely affect the air, water reservoirs, soil and the planet’s biosphere. At Nowadays car engineconsumes about 3 kilogram of atmospheric oxygen when liters of gasoline per 1 kg are burned.Every car delivers 60 m3of gas per hour, and the truck produces 120 m3of gas. These substancesare very dangerous for living organisms and finding solution for the problem of cleaning exhaustedgases is very actual.The purpose of this article is mathematical and numerical modeling on transfer processes in motor-car neutralizer with usage modern programming language and modern computing technologies.The solution of such a problem brings a certain contribution to the protection of the environmentfrom automobile exhaust gases. The task of cleaning at exhaust gases is investigated, that is tosay catalytic oxidation of exhausted gases automobile neutralizer . The mathematical model thereis a system of differential equations warm and mass transfer including heat generation from thechemical reaction. The equation system is solved through numerical methods and to create anddevelop an algorithm of computing the task of cleaning exhaust gases in automobile neutralizer.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Akimbay, Sh.
B19
Balakayeva , G. T
Mathematical and numerical modeling of transfer processes in the cleaning ofexhaust gases in an automobile neutralizer [Текст] / G.T Balakayeva // Әл - Фараби ат. ҚҰУ Хабаршы = Вестник КазНУ им Аль - Фараби. - Алматы, 2018. - №1(97). - Р. 127-133. - (Математика, механика, информатика сериясы=Серия математика, механика, информатика. Journal of Mathematics, Mechanics, Computer Science.)
Рубрики: Информатика
Кл.слова (ненормированные):
нейтрализатор -- каталитический нейтрализатор -- итерационный метод -- метод прогонки
Аннотация: Every year, the atmosphere in Kazakhstan is polluted approximately 5-7 million tons of pollutants,about a third of which belong to the vehicle. Also excess pollution of the air basin of the cities ofthe Republic is caused by pollution of pollutants by metallurgy, oil refining and chemical industryfactories, automobile and railway transport. The harmful substances emitted by motor transportadversely affect the air, water reservoirs, soil and the planet’s biosphere. At Nowadays car engineconsumes about 3 kilogram of atmospheric oxygen when liters of gasoline per 1 kg are burned.Every car delivers 60 m3of gas per hour, and the truck produces 120 m3of gas. These substancesare very dangerous for living organisms and finding solution for the problem of cleaning exhaustedgases is very actual.The purpose of this article is mathematical and numerical modeling on transfer processes in motor-car neutralizer with usage modern programming language and modern computing technologies.The solution of such a problem brings a certain contribution to the protection of the environmentfrom automobile exhaust gases. The task of cleaning at exhaust gases is investigated, that is tosay catalytic oxidation of exhausted gases automobile neutralizer . The mathematical model thereis a system of differential equations warm and mass transfer including heat generation from thechemical reaction. The equation system is solved through numerical methods and to create anddevelop an algorithm of computing the task of cleaning exhaust gases in automobile neutralizer.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Akimbay, Sh.
6.
Подробнее
22.1
L86
Loannis, P.
Qualitative Behavior of the Solutions to Delay and Difference Euations [Текст] / P. Loannis // Әл - Фараби атындағы ҚҰУ Хабаршы = Вестник КазНУ им. Аль - Фараби. - Алматы, 2018. - №2(98). - Р. 3-11. - (Математика, механика, информатика сериясы=Серия математика, механика, информатика. Journal of Mathematics, Mechanics, Computer Science.)
ББК 22.1
Рубрики: Математика
Кл.слова (ненормированные):
oscillation -- delay differential equations -- difference equations
Аннотация: It is noteworthy to observe that a first-order linear ordinary differential equationwithout delaydoes not possess oscillatorysolutions. Therefore the investigation of oscillatory solutions is ofinterest for equations with delays or for the discrete analogue difference equations. Furthermore, themathematical modelling of several real-world problems leads to differential equations that dependon the past history rather than only the current state. In this article conditions are presentedsuch that all solutions of delay and difference equationsare oscillatorywhileall solutionsof thecorresponding ordinary differential equations without delay are, for example,decreasing and tendto zero. Equations with constant and variable arguments are investigated. Several examples ofdelay and difference equations with applications to many sectors of life are presented.
Держатели документа:
ЗКГУ
L86
Loannis, P.
Qualitative Behavior of the Solutions to Delay and Difference Euations [Текст] / P. Loannis // Әл - Фараби атындағы ҚҰУ Хабаршы = Вестник КазНУ им. Аль - Фараби. - Алматы, 2018. - №2(98). - Р. 3-11. - (Математика, механика, информатика сериясы=Серия математика, механика, информатика. Journal of Mathematics, Mechanics, Computer Science.)
Рубрики: Математика
Кл.слова (ненормированные):
oscillation -- delay differential equations -- difference equations
Аннотация: It is noteworthy to observe that a first-order linear ordinary differential equationwithout delaydoes not possess oscillatorysolutions. Therefore the investigation of oscillatory solutions is ofinterest for equations with delays or for the discrete analogue difference equations. Furthermore, themathematical modelling of several real-world problems leads to differential equations that dependon the past history rather than only the current state. In this article conditions are presentedsuch that all solutions of delay and difference equationsare oscillatorywhileall solutionsof thecorresponding ordinary differential equations without delay are, for example,decreasing and tendto zero. Equations with constant and variable arguments are investigated. Several examples ofdelay and difference equations with applications to many sectors of life are presented.
Держатели документа:
ЗКГУ
7.
Подробнее
22.2
L10
Kydyrbekuly, A. B
About the separation of finely divided particles during centrifugation inliquid media [Текст] / A.B Kydyrbekuly // Әл - Фараби ат. ҚҰУ Хабаршы = Вестник КазНУ им Аль - Фараби. - Алматы, 2018. - №2(98). - С. 33-44. - (Математика, механика, информатика сериясы=Серия математика, механика, информатика. Journal of Mathematics, Mechanics, Computer Science.)
ББК 22.2
Рубрики: Механика
Кл.слова (ненормированные):
separation -- settling -- centrifuge -- multiphase fluid -- rotor system -- demetallization of oil
Аннотация: This work is devoted to the study of centrifugation processes, which are one of the most complexprocesses of technology. The use of the action of the centrifugal force field for the separationof heterogeneous liquid systems in a rotor system (centrifuge) is very effective. Separability ofcentrifuged materials, multiphase dispersion, the relationship between phases cause ambiguousprocesses of centrifugation, and therefore it is not always possible to accurately predict and evaluatethe main characteristics of the separation of heterogeneous systems in the centrifugal force field.For a qualitative assessment of the main separation characteristics, such as the angular velocityof rotation, the dependence of the angles of inclination of the glasses on the angular velocity, thesettling time of particles, etc., is created a mathematical model of the vertical rotor system. Therotor represents a round disk on which cups (vial) with a multiphase liquid are symmetricallysuspended. A particular case of a fixed rotor is considered. Nonlinear differential equations ofmotion of the suspension particle, which have no exact solution, are obtained. The research isconducted by analytical and numerical methods. The dependence of the slope angles of the tubesfrom the angular rotational speed of the rotor, sedimentation curves are obtained , which allowestimating the time of particle deposition and the effect of the particle size distribution on theseparation process. The results of this research work allow us to determine with sufficient accuracyall the necessary characteristics of the sedimentation working process, and also, in certain cases,it is possible to exclude the conduct of experimental work. The results of the work confirm thephysical meaning of the process, which can serve as a justification for the use and introduction ofthis mathematical model in industrial production.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Rahmetolla, A.Sh
Ibraev, G.E
L10
Kydyrbekuly, A. B
About the separation of finely divided particles during centrifugation inliquid media [Текст] / A.B Kydyrbekuly // Әл - Фараби ат. ҚҰУ Хабаршы = Вестник КазНУ им Аль - Фараби. - Алматы, 2018. - №2(98). - С. 33-44. - (Математика, механика, информатика сериясы=Серия математика, механика, информатика. Journal of Mathematics, Mechanics, Computer Science.)
Рубрики: Механика
Кл.слова (ненормированные):
separation -- settling -- centrifuge -- multiphase fluid -- rotor system -- demetallization of oil
Аннотация: This work is devoted to the study of centrifugation processes, which are one of the most complexprocesses of technology. The use of the action of the centrifugal force field for the separationof heterogeneous liquid systems in a rotor system (centrifuge) is very effective. Separability ofcentrifuged materials, multiphase dispersion, the relationship between phases cause ambiguousprocesses of centrifugation, and therefore it is not always possible to accurately predict and evaluatethe main characteristics of the separation of heterogeneous systems in the centrifugal force field.For a qualitative assessment of the main separation characteristics, such as the angular velocityof rotation, the dependence of the angles of inclination of the glasses on the angular velocity, thesettling time of particles, etc., is created a mathematical model of the vertical rotor system. Therotor represents a round disk on which cups (vial) with a multiphase liquid are symmetricallysuspended. A particular case of a fixed rotor is considered. Nonlinear differential equations ofmotion of the suspension particle, which have no exact solution, are obtained. The research isconducted by analytical and numerical methods. The dependence of the slope angles of the tubesfrom the angular rotational speed of the rotor, sedimentation curves are obtained , which allowestimating the time of particle deposition and the effect of the particle size distribution on theseparation process. The results of this research work allow us to determine with sufficient accuracyall the necessary characteristics of the sedimentation working process, and also, in certain cases,it is possible to exclude the conduct of experimental work. The results of the work confirm thephysical meaning of the process, which can serve as a justification for the use and introduction ofthis mathematical model in industrial production.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Rahmetolla, A.Sh
Ibraev, G.E
8.
Подробнее
22.2
U93
Utenov, M. U
Determination of displacements in cross-sections of four-bar mechanism linksfrom distributed dynamic loads and their animation using MAPLE [Текст] / M.U Utenov // Әл - Фараби ат. ҚҰУ Хабаршы = Вестник КазНУ им Аль - Фараби. - Алматы, 2018. - №2(98). - Р. 45-56
ББК 22.2
Рубрики: Механика
Кл.слова (ненормированные):
Механизмы -- подвижные стержневые системы -- перемещения -- распределенные динамические нагрузки
Аннотация: The links of high-speed mechanisms and manipulators are deformed under the action of inertiaforces and external loads. These deformations have significantly influence on the accuracy of execu-tion of the required law of motion by the operating point of the mechanism and the positioning ofthe manipulator grip. Accordingly, longitudinal and transverse displacements, angles of rotation ofcross-sections of links under the action of distributed dynamic and external loads are investigatedin this paper. The developed technique allows defining deformations of links of mechanisms andmanipulators and can be applied at their designing. To determine the transverse displacements,the angles of rotation of the cross-sections of the links – the basic differential equation of the elasticline of the beam, to determine the longitudinal displacements of the points of the links – Hooke’slaw and the boundary conditions of the computed scheme of the investigated linkages for elasticcomputation are used. The bending moment in the basic differential equation of the elastic line ofthe beam and the longitudinal force in Hooke’s law were determined by the theory developed bythe authors of the analytical definition of internal forces in the links of planar linkages with stat-ically determinate structures, taking into account the distributed dynamic loads from the massesof links, dead weight and from the acting external loads. According to the developed technique,programs are created in the MAPLE system and animations of the movement of mechanisms arereceived, with the construction on the links the diagrams of transverse, longitudinal displacementsand angles of rotation of the link cross-sections. The developed analytical technique for determin-ing deformations in the cross-sections of links is used to calculate the strength and stiffness ofelements of movable linkages.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Zhilkibayeva, S.K
Baygunchekov, Zh.Zh
U93
Utenov, M. U
Determination of displacements in cross-sections of four-bar mechanism linksfrom distributed dynamic loads and their animation using MAPLE [Текст] / M.U Utenov // Әл - Фараби ат. ҚҰУ Хабаршы = Вестник КазНУ им Аль - Фараби. - Алматы, 2018. - №2(98). - Р. 45-56
Рубрики: Механика
Кл.слова (ненормированные):
Механизмы -- подвижные стержневые системы -- перемещения -- распределенные динамические нагрузки
Аннотация: The links of high-speed mechanisms and manipulators are deformed under the action of inertiaforces and external loads. These deformations have significantly influence on the accuracy of execu-tion of the required law of motion by the operating point of the mechanism and the positioning ofthe manipulator grip. Accordingly, longitudinal and transverse displacements, angles of rotation ofcross-sections of links under the action of distributed dynamic and external loads are investigatedin this paper. The developed technique allows defining deformations of links of mechanisms andmanipulators and can be applied at their designing. To determine the transverse displacements,the angles of rotation of the cross-sections of the links – the basic differential equation of the elasticline of the beam, to determine the longitudinal displacements of the points of the links – Hooke’slaw and the boundary conditions of the computed scheme of the investigated linkages for elasticcomputation are used. The bending moment in the basic differential equation of the elastic line ofthe beam and the longitudinal force in Hooke’s law were determined by the theory developed bythe authors of the analytical definition of internal forces in the links of planar linkages with stat-ically determinate structures, taking into account the distributed dynamic loads from the massesof links, dead weight and from the acting external loads. According to the developed technique,programs are created in the MAPLE system and animations of the movement of mechanisms arereceived, with the construction on the links the diagrams of transverse, longitudinal displacementsand angles of rotation of the link cross-sections. The developed analytical technique for determin-ing deformations in the cross-sections of links is used to calculate the strength and stiffness ofelements of movable linkages.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Zhilkibayeva, S.K
Baygunchekov, Zh.Zh
9.
Подробнее
22.1
K12
Kabanikhin, E. I
Application of differential evolution algorithm for solving the Solow model withthe addition of human capital [Текст] / E.I Kabanikhin // Әл - Фараби ат. ҚҰУ Хабаршы = Вестник КазНУ им Аль - Фараби. - Алматы, 2018. - №2(98). - Р. 57-66. - (Математика, механика, информатика сериясы=Серия математика, механика, информатика. Journal of Mathematics, Mechanics, Computer Science.)
ББК 22.1
Рубрики: Математика
Кл.слова (ненормированные):
economical model -- inverse problems -- optimization -- differential evolution -- Solow model
Аннотация: This paper is devoted to a numerical study of defining of parameters of dynamical systems arisingin financial and economic problems. The importance of parameters that are difficult to measure isgreat, so defining them will help to make forecasts and a work plan for the future at the govern-mental level. An effective way to restore parameters is to solve the inverse problem. The methodof coefficient recovery using the algorithm of differential evolution, which was proposed by RainerStorn and Kenneth Price, is presented in this paper. On the example of solving the direct prob-lem of the mathematical model of neoclassical economic growth of Robert Solow and the resultsobtained, the inverse problem was solved and unknown parameters were determined. The Solowmodel is based on the Cobb-Douglas production function, taking into account labor, capital andexogenous neutral technical progress. Also, for further calculations, the economic model proposedby Mankiw-Romer-Weil based on the Solow model was considered, but with the addition of hu-man capital, where the number of variables and coefficients that need to be restored has alreadyincreasing. A direct problem was also solved, results were obtained that were applied in the algo-rithm of differential evolution for parameters recovery.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Bektemessov, M.A
Shishlenin, M.A
Yang Xin-She
Bektemessov, Zh.M
K12
Kabanikhin, E. I
Application of differential evolution algorithm for solving the Solow model withthe addition of human capital [Текст] / E.I Kabanikhin // Әл - Фараби ат. ҚҰУ Хабаршы = Вестник КазНУ им Аль - Фараби. - Алматы, 2018. - №2(98). - Р. 57-66. - (Математика, механика, информатика сериясы=Серия математика, механика, информатика. Journal of Mathematics, Mechanics, Computer Science.)
Рубрики: Математика
Кл.слова (ненормированные):
economical model -- inverse problems -- optimization -- differential evolution -- Solow model
Аннотация: This paper is devoted to a numerical study of defining of parameters of dynamical systems arisingin financial and economic problems. The importance of parameters that are difficult to measure isgreat, so defining them will help to make forecasts and a work plan for the future at the govern-mental level. An effective way to restore parameters is to solve the inverse problem. The methodof coefficient recovery using the algorithm of differential evolution, which was proposed by RainerStorn and Kenneth Price, is presented in this paper. On the example of solving the direct prob-lem of the mathematical model of neoclassical economic growth of Robert Solow and the resultsobtained, the inverse problem was solved and unknown parameters were determined. The Solowmodel is based on the Cobb-Douglas production function, taking into account labor, capital andexogenous neutral technical progress. Also, for further calculations, the economic model proposedby Mankiw-Romer-Weil based on the Solow model was considered, but with the addition of hu-man capital, where the number of variables and coefficients that need to be restored has alreadyincreasing. A direct problem was also solved, results were obtained that were applied in the algo-rithm of differential evolution for parameters recovery.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Bektemessov, M.A
Shishlenin, M.A
Yang Xin-She
Bektemessov, Zh.M
10.
Подробнее
32.81
T96
Turar, O. N
Design of adaptive unstructured grids using differential methods [Текст] / O.N Turar // Әл - Фараби ат. ҚҰУ Хабаршы = Вестник КазНУ им Аль - Фараби. - Алматы, 2018. - №2(98). - Р. 88-97. - (Математика, механика, информатика сериясы=Серия математика, механика, информатика. Journal of Mathematics, Mechanics, Computer Science.)
ББК 32.81
Рубрики: Информатика
Кл.слова (ненормированные):
computational grid construction algorithm -- unstructured mesh -- adaptive mesh -- differential elliptic equations -- reversed Beltrami equation
Аннотация: Adaptive generation of computational grids can improve the efficiency of mathematical model-ing by increasing the accuracy of numerical approximations. The paper describes a method forconstructing unstructured grids with adaptation based on differential methods. The applicationof these methods ensures a smooth distribution of the geometric characteristics of the grid, i.e.the appearance of adjacent cells that differ greatly in size and shape becomes unlikely. To achieveproper adaptation in unstructured grids we use the novel approach based on methodology of adap-tive structured grid construction. This approach uses the method of grid construction based onsolving inverted Beltrami equation to create mapping of some sample grid domain to the physicalarea. This mapping is used to construct point set on which the unstructured grid is constructedusing Delaunay triangulation method. Thus, the result is unstructured grid with proper adapta-tion. Adding fault and fractures or other structure elements may be supported by implementingconstrained Delaunay triangulation.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Akhmed-Zaki, D.Zh
T96
Turar, O. N
Design of adaptive unstructured grids using differential methods [Текст] / O.N Turar // Әл - Фараби ат. ҚҰУ Хабаршы = Вестник КазНУ им Аль - Фараби. - Алматы, 2018. - №2(98). - Р. 88-97. - (Математика, механика, информатика сериясы=Серия математика, механика, информатика. Journal of Mathematics, Mechanics, Computer Science.)
Рубрики: Информатика
Кл.слова (ненормированные):
computational grid construction algorithm -- unstructured mesh -- adaptive mesh -- differential elliptic equations -- reversed Beltrami equation
Аннотация: Adaptive generation of computational grids can improve the efficiency of mathematical model-ing by increasing the accuracy of numerical approximations. The paper describes a method forconstructing unstructured grids with adaptation based on differential methods. The applicationof these methods ensures a smooth distribution of the geometric characteristics of the grid, i.e.the appearance of adjacent cells that differ greatly in size and shape becomes unlikely. To achieveproper adaptation in unstructured grids we use the novel approach based on methodology of adap-tive structured grid construction. This approach uses the method of grid construction based onsolving inverted Beltrami equation to create mapping of some sample grid domain to the physicalarea. This mapping is used to construct point set on which the unstructured grid is constructedusing Delaunay triangulation method. Thus, the result is unstructured grid with proper adapta-tion. Adding fault and fractures or other structure elements may be supported by implementingconstrained Delaunay triangulation.
Держатели документа:
ЗКГУ
Доп.точки доступа:
Akhmed-Zaki, D.Zh
Страница 1, Результатов: 26